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Factor.\newline2w2+9w+72w^2 + 9w + 7

Full solution

Q. Factor.\newline2w2+9w+72w^2 + 9w + 7
  1. Identify coefficients: Identify the coefficients aa, bb, and cc in the quadratic expression 2w2+9w+72w^2 + 9w + 7 by comparing it to the standard form ax2+bx+cax^2 + bx + c.a=2a = 2, b=9b = 9, c=7c = 7
  2. Find suitable numbers: Find two numbers that multiply to aca*c (27=142*7 = 14) and add up to bb (99).\newlineThe numbers that satisfy these conditions are 22 and 77 because 27=142*7 = 14 and 2+7=92+7 = 9.
  3. Rewrite middle term: Rewrite the middle term 9w9w using the two numbers found in the previous step.\newline2w2+9w+72w^2 + 9w + 7 can be rewritten as 2w2+2w+7w+72w^2 + 2w + 7w + 7.
  4. Factor by grouping: Factor by grouping. Group the first two terms and the last two terms.\newline(2w2+2w)+(7w+7)(2w^2 + 2w) + (7w + 7)
  5. Factor out common factor: Factor out the greatest common factor from each group. 2w(w+1)+7(w+1)2w(w + 1) + 7(w + 1)
  6. Final factorization: Since both groups contain the common factor (w+1)(w + 1), factor this out.(2w+7)(w+1)(2w + 7)(w + 1)